Generalized correlation function: definition, properties, and application to blind equalization

• Published in: IEEE transactions on signal processing Vol. 54; no. 6; pp. 2187 - 2197
• Main Authors: Santamaria, I., Pokharel, P.P., Principe, J.C.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01-06-2006; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithm design and analysis; Applied sciences; Blind equalization; Blind equalizers; Blinds; Correlation; Detection, estimation, filtering, equalization, prediction; Entropy; Equalization; Exact sciences and technology; generalized correlation kernel; Hilbert space; information theoretic learning; Information theory; Information, signal and communications theory; Kernel; Kernels; Learning; reproducing kernel Hilbert space (RKHS); Shape measurement; Signal and communications theory; Signal processing algorithms; Signal, noise; Statistical distributions; Stochastic processes; Telecommunications and information theory; Time measurement; Time series; Performance evaluation; information theoretic learning; Statistical distribution; Generalized function; Time series; Stochastic process; Blind equalization; Kernel method; Learning; entropy; Cavity; reproducing kernel Hilbert space (RKHS); Correlation function; generalized correlation kernel; Information theory
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/TSP.2006.872524

With an abundance of tools based on kernel methods and information theoretic learning, a void still exists in incorporating both the time structure and the statistical distribution of the time series in the same functional measure. In this paper, a new generalized correlation measure is developed that includes the information of both the distribution and that of the time structure of a stochastic process. It is shown how this measure can be interpreted from a kernel method as well as from an information theoretic learning points of view, demonstrating some relevant properties. To underscore the effectiveness of the new measure, a simple blind equalization problem is considered using a coded signal.